How does limewire know how many hosts are on?

Why do they monitor it

If you are asking about http://www.limewire.com/english/content/netsize.shtml those stats haven't worked well for months, and are are quite inaccurate.

Why does LimeWire try to measure the size of the network? Probably for the same reasons other networks do--to be able to judge the effectiveness of the development of features outside of the labs.

Making a change that affects a few hundred people is one thing: changing something that affects millions of people around the world is something else.